One of my favorite YouTube channels to learn film making is RocketJump Film School. I definitely recommend this channel for any level of filmmaker. Understanding cuts and transitions is important in story telling. Think of it as a puzzle. In order to see the big picture. You have to fit the pieces together. Cuts and transitions help flow the story. In the video above, it explains the varieties of cuts and transitions.
One common use of cuts is the cutting on action. Cutting on action is basically self explanatory. You cut on action. A person could be rushing into a door. As the person opens the door, it cuts to the other side of the door to complete the action. The action is the person opening the door and entering it. The cut pieces two different shots together to complete the action.
Moving on to transitions, a common transition used in most films is the fade in\out. The fade in and fade out is a transitions that basically fades the screen to black or the opposite. The fade is a transition that either changes the scene from one to another, or it's the beginning of a new scene.
Cuts and transitions are important in story telling. Understanding how to use them helps flow the story. Without them the story would feel disconnected, distracting and boring. Watch the video above from RocketJump Film School to get an understanding of the variety of cuts and transitions out there.